Identification of Musical Instruments by means of the - - PowerPoint PPT Presentation

▶
identification of musical instruments by means of the
SMART_READER_LITE
LIVE PREVIEW

Identification of Musical Instruments by means of the - - PowerPoint PPT Presentation

Dec 24, 2023 179 likes •435 views

Identification of Musical Instruments by means of the Hough-Transformation over 1 , Frank Klefenz 2 and Claus Weihs 1 Christian R 1 Fachbereich Statistik Universit at Dortmund 44221 Dortmund, Germany roever@statistik.uni-dortmund.de 2

slide-1
SLIDE 1

Identification of Musical Instruments by means of the Hough-Transformation

Christian R¨

  • ver1, Frank Klefenz2 and Claus Weihs1

1 Fachbereich Statistik

Universit¨ at Dortmund 44221 Dortmund, Germany roever@statistik.uni-dortmund.de

2 Fraunhofer-Institut f¨

ur Digitale Medientechnologie Langewiesener Straße 22 98693 Ilmenau, Germany March 9, 2004

slide-2
SLIDE 2

Overview

1. the Hough-transform 2. application to sound data 3. resulting data format 4. classification approaches 5. results

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

1

slide-3
SLIDE 3

The Hough-transform

  • originally developed for image processing1: detection of straight lines,

later generalized to arbitrary functions/shapes2

  • similar to regression

– robust – simultaneous fitting of several lines possible

1Hough, P.V.C. (1959): Machine analysis of bubble chamber pictures. In: International conference on

high-energy accelerators and instrumentation. Gen` eve, 554-556.

2Shapiro, S.D. (1978): Feature Space Transforms for Curve Detection. Pattern Recognition, 10, 129–143. Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

2

slide-4
SLIDE 4

Audio data

  • apply to (digital) audio data
  • motivation: characterize sounds by oscillation pattern

➜ does that lead to useful sound characterization? ➜ check by trying to recognize sounds

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

3

slide-5
SLIDE 5

time (s) amplitude 0.380 0.382 0.384 0.386 0.388 0.390 −0.4 0.0 0.4 0.8 | |

period

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

4

slide-6
SLIDE 6

time (s) amplitude 0.380 0.382 0.384 0.386 0.388 0.390 −0.4 0.0 0.4 0.8 | |

period

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

5

slide-7
SLIDE 7

Transform parameter setting

  • focus on signal edges
  • fit a sinusoidal function to sound samples:

f(t) = A · sin(2πc · t − ϕ) (ϕ ≤ t ≤ ϕ + 1

4c)

A ≥ 1 : amplitude − → slope ϕ ≥ 0 : phase difference − → time c : center frequency (fixed)

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

6

slide-8
SLIDE 8

f(t) = A · sin(2πc · t − ϕ)

1 4c

1 f(t) t φ A

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

7

slide-9
SLIDE 9

time (s) amplitude 0.380 0.382 0.384 0.386 0.388 0.390 0.0 0.5 1.0

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

8

slide-10
SLIDE 10

Resulting data

  • transformed sound is another time series:

phase difference ϕ amplitude A Nr. sample seconds class-nr. value . . . . . . . . . . . . . . . 104 16731 0.3793881 28 1.163636 105 16838 0.3818141 31 1.049180 106 16894 0.3830841 22 1.488372 107 19896 0.3831291 25 1.306122 108 17004 0.3855781 30 1.084746 109 17065 0.3869611 27 1.207547 110 17173 0.3894101 31 1.049180 . . . . . . . . . . . . . . .

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

9

slide-11
SLIDE 11

Amplitude (A) and Frequency

  • 1

ϕt − ϕt−1

  • ver time

time (s) amplitude (class nr.) 5 15 25 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 20 200 2000 50000 time (s) frequency (Hz) Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

10

slide-12
SLIDE 12

time (s) amplitude (class nr.) 0.0 0.2 0.4 0.6 5 10 15 20 25 30

piano a4 (440 Hz)

time (s) amplitude (class nr.) 0.0 0.2 0.4 0.6 5 10 15 20 25 30

piano b4 (466 Hz)

time (s) amplitude (class nr.) 0.0 0.2 0.4 0.6 5 10 15 20 25 30

trumpet a4 (440 Hz)

time (s) amplitude (class nr.) 0.0 0.2 0.4 0.6 5 10 15 20 25 30

trumpet b4 (466 Hz)

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

11

slide-13
SLIDE 13

Classification

➜ How can we use transformed data for classification?

  • first approach:

do frequencies of the 32 possible amplitude values yield a sufficient (‘spectrum-like’) sound characterization?

  • second approach:

derive characterizing variables – characterize (marginal) distributions of amplitudes and frequencies – characterize distribution over time: autocorrelation and trend – . . .

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

12

slide-14
SLIDE 14

First approach

time (s) amplitude (class nr.) 0.0 0.2 0.4 0.6 5 10 15 20 25 30

➜ 32 variables + pitch = 33 total

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

13

slide-15
SLIDE 15

Second approach

  • transform durations between signal edges into frequencies
  • mean amplitude, mean frequency
  • amplitude trend over time
  • autocorrelation of amplitudes
  • . . .

➜ 62 variables total

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

14

slide-16
SLIDE 16

Data

  • investigated data set3: 1987 digitized sounds

(CD-quality — 44.1 kHz, 16 bit, mono) pitches are given

  • 62 sequences of ≈32 sounds
  • sequences of sounds by same or similar instruments were grouped together

(e.g. piano at different volumes or bassoon and contrabassoon) ➜ 25 instrument classes

3Opolko, F., Wapnick, J.: McGill University Master Samples (CD-Set). 1987.

See http://www.music.mcgill.ca/resources/mums/html/

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

15

slide-17
SLIDE 17

Applied methods

  • LDA: Linear Discriminant Analysis
  • QDA: Quadratic Discriminant Analysis
  • naive Bayes
  • RDA: Regularized Discriminant Analysis
  • Support Vector Machine
  • Classification Tree
  • k-NN: k-Nearest-Neighbour

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

16

slide-18
SLIDE 18

Regularized Discriminant Analysis (RDA)4

  • QDA-like; covariance matrix is manipulated using two parameters
  • only one of them improved classification
  • class k covariance matrix estimate reduces to:

ˆ ΣRDA

k

= λˆ ΣLDA + (1 − λ)ˆ ΣQDA

k

(0 ≤ λ ≤ 1)

  • λ = 0

→ QDA λ = 1 → LDA

4Friedman, J.H. (1989): Regularized Discriminant Analysis. Journal of the American Statistical

Association, 84, No. 405, 165–175

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

17

slide-19
SLIDE 19

Variable selection

  • necessary for second approach (not appropriate in first approach)
  • performed iteratively in a stepwise manner:

– start with pitch only – in every step include variable that leads to greatest misclassification rate improvement – misclassification rate estimated by cross-validation

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

18

slide-20
SLIDE 20

RDA-parameter tuning

λ misclassification rate (%) 25 30 35 40 45 QDA 0.2 0.4 0.6 0.8 LDA

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

19

slide-21
SLIDE 21

Applied methods

  • first approach (amplitude frequencies):

best result: 66% error rate using k-Nearest-Neighbour

  • second approach (characterizing variables):

final result: 26.1% error rate using Regularized Discriminant Analysis (RDA) with 11 variables and λ = 0.1

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

20

slide-22
SLIDE 22

Discriminating features

  • pitch
  • waiting time for first edge and sound duration
  • signal edge rate (per second)
  • mean, variance and shape of amplitude distribution
  • trend of amplitudes
  • mean and variance of frequency distribution
  • correlation of amplitude and frequency

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

21

slide-23
SLIDE 23

Comparing the results

  • final misclassification rate: 26.1%
  • misclassification rate by guessing: 24

25 = 96%

  • rates achieved by humans: ≈ 44%
  • rates by automatic recognition5: ≈ 19 – 7.2%

5Bruderer,

M.J. (2003): Automatic recognition of musical instruments, Masters Thesis, Ecole Polytechnique Federale de Lausanne.

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

22

slide-24
SLIDE 24

Conclusions

➜ Hough-transformation yields useful characterization of a sound ➜ classification results achieved with RDA better than human, still worse than with other approaches (comparable?)

  • open questions:

noise sensitivity?

  • ther transform parameter settings?

. . .

Christian R¨

  • ver, Frank Klefenz and Claus Weihs: Identification of Musical Instruments by means of the Hough-Transformation

23